Structural Zeros and Their Implications With Log‐Linear Bivariate Presmoothing Under the Internal‐Anchor Design

In equating, when common items are internal and scoring is conducted in terms of the number of correct items, some pairs of total scores ( X ) and common‐item scores ( V ) can never be observed in a bivariate distribution of X and V ; these pairs are called structural zeros . This simulation study examines how equating results compare for different approaches to handling structural zeros. The study considers four approaches: the no‐smoothing, unique‐common, total‐common, and adjusted total‐common approaches. This study led to four main findings: (1) the total‐common approach generally had the worst results; (2) for relatively small effect sizes, the unique‐common approach generally had the smallest overall error; (3) for relatively large effect sizes, the adjusted total‐common approach generally had the smallest overall error; and, (4) if sole interest focuses on reducing bias only, the adjusted total‐common approach was generally preferable. These results suggest that, when common items are internal and log‐linear bivariate presmoothing is performed, structural zeros should be maintained, even if there is some loss in the moment preservation property.